Question: Simplify the following expression: $z = \dfrac{2r^2 - 20r + 32}{r - 8} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $2$ , so we can rewrite the expression: $ z =\dfrac{2(r^2 - 10r + 16)}{r - 8} $ Then we factor the remaining polynomial: $r^2 {-10}r + {16} $ ${-8} {-2} = {-10}$ ${-8} \times {-2} = {16}$ $ (r {-8}) (r {-2}) $ This gives us a factored expression: $\dfrac{2(r {-8}) (r {-2})}{r - 8}$ We can divide the numerator and denominator by $(r + 8)$ on condition that $r \neq 8$ Therefore $z = 2(r - 2); r \neq 8$